Prize for Stability and Market Design

It was a pleasure to awaken to the news that this years Nobel (memorial) in Economics went to Shapley and Roth (Schwartz lecture series hits bullseye again). Even more had it gone to me…..but, have yet to see pigs in the sky.

Pleasure turned to amusement as I heard and read the attempts of journalists to summarize the contributions honored. NPR suggested that it was about applying statistics. Forbes had a piece that among Indians would be described as putting shit in milk. This always makes me wonder about the other things they get wrong in the subjects I have no knowledge of. Nevertheless, I will plug one outlet for reasons that will become obvious upon reading it.

In this post, I set myself the task of seeing if I can do a better job than the fourth estate of conveying the nature of the contribution that was honored, Oct 15th, 2012. Here goes.

The fictional decentralized markets of the textbook, like the frictionless plane in a vacuum used in physics, are a useful device for establishing a benchmark. Real markets, however, must deal with frictions and the imperfections of their participants. One such market is for College Admissions in the US that is largely decentralized This decentralization increases uncertainty and raises costs. Students, for example, must forecast which colleges are likely to accept them. The greater the uncertainty in these forecasts the more `insurance’ is purchased either by applying to a large set of colleges or aiming `low’. On the college side, this insurance makes yields difficult to forecast. Increasing acceptance rates to increase yields has the effect of driving application numbers in the future down, so, waiting lists grow. These problems could be eliminated were one to switch to a centralized admissions market. How would one design such a centralized process? This is the question that the work of Shapley (and the late David Gale) and Alvin Roth addresses.

A major hurdle that a centralized market for college admissions must overcome is that it must match students with colleges in a way that respects the preferences and incentives of both parties. A centralized market cannot force a student to attend a college she does not want to, or require a college to accept a particular student. There is always the threat that the participants can pick up their marbles and walk away. If enough do, the incentives for the students and colleges that participate in the centralized market decline. Would a student participate in an centralized market if certain brand name colleges opted out? The work of (Gale &) Shapley was the first to formalize this concern with designing centralized markets that would be immune defections on the part of participants, i.e., stable. Their seminal paper articulated a model and a mechanism for matching students to colleges that would be stable in this sense. Alvin Roth’s own work builds on this in a number of ways. The first is to use the notion of stability to explain why some centralized markets fail. Second, to highlight the importance of other sources of instability associated with, say timing. Participants may wish to `jump the clock’. Colleges, for example, offering admission to high school students in their junior year when there might be less competition for that student. The third, is to use the ideas developed in other contexts to allocate scarce resources where money as a medium of exchange is ruled out, most notably kidneys.

The work honored this year has its roots in a specialty of game theory, long considered unfashionable but one Shapley made deep contributions to: co-operative game theory. One can trace an unbroken line between the concern for stability in the design for markets and the abstract notions of stability discussed, for example, in the first book on game theory by von-Neuman and Morgenstern. It proves, once again, Keynes’ dictum:

“The power of vested interests is vastly exaggerated compared with the gradual encroachment of ideas.’’

Yes, shorter, but, I think inaccurate. In the absence of prices we know what will happen….barter. If one takes the word `design’ seriously it presumes the ability to set standards and terms that participants will subscribe to. For example, we agree to use medium of exchange called money. Why should we do so? What if a subset of us would be better off peeling off and trading among themselves? These are questions that arise in markets that use money (think of the rise of dark pools in financial markets) as well as those that don’t.

You’ve caught me.The answer to your immediate question, is yes we can have free rider problems with just ordinal preferences. I should have said: I don’t think the prize is just about understanding markets where the only information one has are preferences. While the applications that Roth is celebrated for are to markets where money is ruled out (or there are imperfect substitutes for it), the ideas about stability etc apply also to markets with transfers (think of the Shapley-Shubik model).

[…] more information, see the blog entries by professors Jeff Ely in Cheap Talk and Rakesh Vohra in The Leisure on the Theory Class. Al Roth blogs at Market Design. MoreLike this:LikeBe the first to like […]